I especially recommend a long walk in rural or small-town Japan. Perhaps the best one-day option is the Yamanobe Road
https://www.japan.travel/en/destinations/kansai/nara/the-yam...
which is breathtaking. You pass ancient tombs, temples, and shrines -- you will have beautiful mountains to your east and even more beautiful small towns to your west. If you've seen My Neighbor Totoro, imagine that it was brought to life and you got to spend all day walking through it. It's fairly easy to get to from Nara, Osaka, or Kyoto.
If you have more time, the classic long-distance walk in Japan is the Henro-michi in Shikoku, aka the Shikoku pilgrimage.
https://shikoku-tourism.com/en/shikoku-henro/shikoku-henro
I did it on foot over 58 days, and it was absolutely the experience of a lifetime. Even if you don't have two months, just a few days on the trail will showcase rural Japan at its most beautiful, and the Japanese people at their friendliest and most welcoming.
Oh -- and I've driven in Japan, but you'll probably want to get around by train instead, the mass transit is the best in the world.